From 920fbc095386afd4dfcd95d85ef7ef9072b3d5d7 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Thu, 13 Jul 2017 15:05:55 +0530 Subject: Modified Engineering_Mechanics/ --- Engineering_Mechanics/chapter_9.ipynb | 1623 +++++++++++++++++++++++++++++++++ 1 file changed, 1623 insertions(+) create mode 100644 Engineering_Mechanics/chapter_9.ipynb (limited to 'Engineering_Mechanics/chapter_9.ipynb') diff --git a/Engineering_Mechanics/chapter_9.ipynb b/Engineering_Mechanics/chapter_9.ipynb new file mode 100644 index 00000000..73d7ecff --- /dev/null +++ b/Engineering_Mechanics/chapter_9.ipynb @@ -0,0 +1,1623 @@ +{ + "metadata": { + "name": "chapter_9.ipynb" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9:Lifting Machines" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1,Page No.295" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P=100 #N #effort applied\n", + "W=900 #N #Lad applied\n", + "y=100 #cm #Distance moved by effort\n", + "x=10 #cm #Distance moved by load\n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio \n", + "VR=y*x**-1 \n", + "\n", + "#Efficiency\n", + "rho=MA*VR**-1*100\n", + "\n", + "#Result\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"velocity ratio is\",round(VR,2)\n", + "print\"Efficiency is\",round(rho,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical Advantage is 9.0\n", + "velocity ratio is 10.0\n", + "Efficiency is 90.0\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2,Page No.296" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P=500 #N #Effort applied\n", + "y=5 #m #Distance moved by effort\n", + "x=0.5 #cm #Distance moved by load\n", + "rho=0.8 #Efficiency\n", + "\n", + "#Calculations\n", + "\n", + "#Load Lifted by machine\n", + "W=P*y*rho*(x)**-1 #N\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=y*x**-1 \n", + "\n", + "#Result\n", + "print\"Load Lifted by the machine is\",round(W,2),\"N\"\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"Velocity ratio is\",round(VR,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Load Lifted by the machine is 4000.0 N\n", + "Mechanical Advantage is 8.0\n", + "Velocity ratio is 10.0\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3,Page No.297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P=20 #N #Actual Effort\n", + "W=900 #N #Load Lifted\n", + "y=2.40 #m #Distance moved by effort\n", + "x=0.04 #m #Distance moved by load\n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=y*x**-1 \n", + "\n", + "#Efficiency\n", + "rho=MA*VR**-1\n", + "\n", + "#Ideal Effort required\n", + "P1=rho*P \n", + "\n", + "#Result\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Efficiency is\",round(rho,2)\n", + "print\"Ideal Effort is\",round(P1,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical Advantage is 45.0\n", + "Velocity ratio is 60.0\n", + "Efficiency is 0.75\n", + "Ideal Effort is 15.0\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4,Page No.297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "rho=0.7 #eifficiency\n", + "P=10 #N #Effort\n", + "W=500 #N #Load\n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=MA*rho**-1\n", + "\n", + "#Result\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"Velocity ratio is\",round(VR,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical Advantage is 50.0\n", + "Velocity ratio is 71.43\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5,Page No.299" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P1=15 #N #Effort\n", + "W1=770 # #Load\n", + "rho=0.60 #Efficiency\n", + "\n", + "P2=25 #N \n", + "W2=1320\n", + "\n", + "P=15 #N \n", + "W=500 #N\n", + "\n", + "#Calculations\n", + "\n", + "#First Case\n", + "\n", + "#Mechanical Advantage\n", + "MA=W1*P1**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=MA*rho**-1 \n", + "\n", + "#Second case\n", + "\n", + "#Mechanical Advantage\n", + "MA2=W2*P2**-1 \n", + "\n", + "#Efficiency\n", + "rho2=MA2*VR**-1*100\n", + "\n", + "#Third case\n", + "\n", + "#from LAw of machine\n", + "#P=m*W+C ................1\n", + "\n", + "#Equation 2\n", + "#P2=W2*m+C ...............2\n", + "\n", + "#Subtracting equation 2 from 1 we get\n", + "m=10*550**-1\n", + "\n", + "#Constacnt value \n", + "C=P2-W2*m\n", + "\n", + "#Sub value C in equation 1 we get\n", + "P3=m*W+C #N\n", + "\n", + "#MAx Mechanical advantage\n", + "MA_max=1*m**-1\n", + "\n", + "#MAx Efficiency \n", + "rho_max=1*(m*VR)**-1*100\n", + "\n", + "#Result\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"Velocity Ratio is\",round(VR,2)\n", + "print\"Efficiency is\",round(rho2,2),\"%\"\n", + "print\"Effort Required to raise the Load 500 N\",round(P3,2),\"N\"\n", + "print\"MAx Mechanical Advantage is\",round(MA_max,2)\n", + "print\"MAx Efficiency is\",round(rho_max,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical Advantage is 51.33\n", + "Velocity Ratio is 85.56\n", + "Efficiency is 61.71 %\n", + "Effort Required to raise the Load 500 N 10.09 N\n", + "MAx Mechanical Advantage is 55.0\n", + "MAx Efficiency is 64.29\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6,Page No.301" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "#Effort\n", + "P1=15.5 #N\n", + "P2=19.5 #N\n", + "\n", + "#Loads\n", + "W1=100 #N\n", + "W2=90 #N\n", + "\n", + "m=0.2\n", + "\n", + "#Calculations\n", + "\n", + "#Law of machine equation \n", + "#P=m*W+C \n", + "\n", + "#Equations\n", + "#P1=m*W1+C ................1\n", + "#P2=m*W2+C ....................2\n", + "\n", + "#sub value of m in equation 1 weget\n", + "C=P1-m*W1\n", + "\n", + "#Effort required to lift a Load\n", + "P1=m*W1+C\n", + "\n", + "#MEchanical advantage\n", + "MA=1*m**-1\n", + "\n", + "#Result\n", + "print\"Effort required to Lift a Load of 100 N\",round(P1,2),\"N\"\n", + "print\"MAx MEchanical Advantage is\",round(MA,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort required to Lift a Load of 100 N 15.5 N\n", + "MAx MEchanical Advantage is 5.0\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.7,Page No.303" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "rho=0.8 #Efficiency\n", + "P=15 #N #Effort\n", + "W=130 #N #Load\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=W*(P*rho)**-1 \n", + "\n", + "#Frictional force in terms of machine in tems of effort\n", + "Fp=P-W*VR**-1 #N\n", + "\n", + "#Frictional Force of the machine in terms of Load\n", + "Fw=P*VR-W #N\n", + "\n", + "#Result\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Frictional force in terms of machine in tems of effort\",round(Fp,2),\"N\"\n", + "print\"Frictional Force of the machine in terms of Load is\",round(Fw,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity ratio is 10.83\n", + "Frictional force in terms of machine in tems of effort 3.0 N\n", + "Frictional Force of the machine in terms of Load is 32.5 N\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.8,Page No.303" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "VR=15 #Velocity ratio\n", + "rho=0.6 #Efficiency\n", + "W=100 #N #Load Lifted\n", + "\n", + "#Calculations\n", + "\n", + "#Power\n", + "P=W*(VR*rho)**-1 #N\n", + "\n", + "#Frictional Force\n", + "Fp=P-(W*VR**-1) #N\n", + "\n", + "#Let C=Fp\n", + "C=Fp\n", + "\n", + "#From law of machine,we get\n", + "#P=m*W+C\n", + "#After sub values and furter simplifying we get\n", + "m=(P-C)*W**-1\n", + "\n", + "#After sub values in above equaion we get law of machine as\n", + "#P2=m*W2+c #N\n", + "\n", + "#when W2=140 #N\n", + "W2=140 #N\n", + "P2=m*W2+C #N\n", + "\n", + "#When W3=0\n", + "W3=0 #N\n", + "P3=m*W3+C #N\n", + "\n", + "#Result\n", + "print\"Effort required to run the machine at Load:W2=140 is\",round(P2,2),\"N\"\n", + "print\"Effort required to run the machine at Load:W3=0 is\",round(P3,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort required to run the machine at Load:W2=140 is 13.78 N\n", + "Effort required to run the machine at Load:W3=0 is 4.44 N\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.9,Page No.304" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P=12 #N #Effort\n", + "VR=18 #Velocity ratio\n", + "rho=0.6 #efficiency\n", + "\n", + "#Calculations\n", + "\n", + "#Load lifted\n", + "W=rho*P*VR #N\n", + "\n", + "#LEt C=Fp\n", + "Fp=P-(W*VR**-1) #N\n", + "C=Fp\n", + "\n", + "#From law of machine we get\n", + "m=(P-C)*W**-1 #N\n", + "\n", + "#Sub value of m in equation we get\n", + "#P2=1*18**-1*W2+C\n", + "\n", + "#Sub W2=90\n", + "W2=90 \n", + "P2=m*W2+C\n", + "\n", + "\n", + "#Result\n", + "print\"Effort required to run the machine is\",round(P2,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort required to run the machine is 9.8 N\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.10,Page No.305" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "VR=10 #Velocity ratio\n", + "P=100 #N #Effort applied\n", + "Fp=20 #N #effort lost in friction\n", + "\n", + "#Calculations\n", + "\n", + "#Load Lifted\n", + "W=(P-Fp)*VR #N\n", + "\n", + "#Efficiency\n", + "rho=W*P**-1*VR**-1*100 \n", + "\n", + "#Result\n", + "print\"Load Lifted is\",round(W,2),\"N\"\n", + "print\"Efficiency is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Load Lifted is 800.0 N\n", + "Efficiency is 80.0 %\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.11,Page No.305" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "P=40 #N #Effort applied\n", + "W=600 #N #Load Lifted\n", + "VR=20 #Velocity ratio\n", + "\n", + "#Calculations\n", + "\n", + "#MAchine Fiction in terms of effort\n", + "Fp=P-W*VR**-1 #N\n", + "\n", + "#M/c Friction in terms of Load\n", + "Fw=P*VR-W #N\n", + "\n", + "#efficiency\n", + "rho=W*P**-1*VR**-1*100\n", + "\n", + "#Result\n", + "print\"MAchine Fiction in terms of effort is\",round(Fp,2),\"N\"\n", + "print\"M/c Friction in terms of Load is\",round(Fw,2),\"N\"\n", + "print\"Ffficiency of the machine is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "MAchine Fiction in terms of effort is 10.0 N\n", + "M/c Friction in terms of Load is 200.0 N\n", + "Ffficiency of the machine is 75.0 %\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.12,Page No.306" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "P=15 #N #Effort applied\n", + "W=200 #N #Load Lifted\n", + "VR=40 #Velocity ratio\n", + "\n", + "#Calculations\n", + "\n", + "#Efficiency\n", + "rho=W*P**-1*VR**-1 #%\n", + "\n", + "#Friction Load of m/c \n", + "Fw=P*VR-W #N\n", + "\n", + "#Result\n", + "print\"Friction Load of m/c is\",round(Fw,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Friction Load of m/c is 400.0 N\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.13,Page No.307" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=48 #N #Weight\n", + "P=16 #N #Force\n", + "D=400 #mm #Diameter of wheel\n", + "d=100 #mm #Diameter of axle\n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=D*d**-1 \n", + "\n", + "#Efficiency of the machine\n", + "rho=MA*VR**-1*100 #%\n", + "\n", + "#Result\n", + "print\"Mechanical Advantage is\",round(MA,2)\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Efficiency of the machine is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical Advantage is 3.0\n", + "Velocity ratio is 4.0\n", + "Efficiency of the machine is 75.0 %\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.14,Page No.309" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "D=25 #cm #Diameter of wheel\n", + "d1=10 #cm #LArge dia. of axle\n", + "d2=9 #cm #Small Dia. of axle\n", + "P=30 #N #Effort applied\n", + "W=900 #N #Load Lifted\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*D*(d1-d2)**-1 \n", + "\n", + "#Mechanical advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Efficiency\n", + "rho=MA*VR**-1*100\n", + "\n", + "#Result\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Mechanical advantage is\",round(MA,2)\n", + "print\"Efficiency is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity ratio is 50.0\n", + "Mechanical advantage is 30.0\n", + "Efficiency is 60.0 %\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.15,Page No.310" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "T=60 #No. of teeth on worm wheel\n", + "L=12.5 #cm #Radius of effort wheel\n", + "r=6.25 #cm #Radius of Load drum\n", + "P=20 #N #Effort\n", + "W=600 #N #Load\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=L*T*r**-1 \n", + "\n", + "#Efficiency\n", + "rho=W*P**-1*VR**-1*100\n", + "\n", + "#Result\n", + "print\"Velocity ratio for single threaded worm is\",round(VR,2)\n", + "print\"Efficiency of the worm is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity ratio for single threaded worm is 120.0\n", + "Efficiency of the worm is 25.0 %\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.16,Page No.312" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "T1=10 #No.of teeth on pinion\n", + "T2=100 #No.of teeth on spur wheel\n", + "D=30 #cm #Dia. of Load axle\n", + "L=30 #cm #Length of lever\n", + "P=20 #N #Effort applied\n", + "W=360 #N #Load Lifted\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*L*T2*(D*T1)**-1\n", + "\n", + "#Efficiency\n", + "rho=W*P**-1*VR**-1*100\n", + "\n", + "#Result\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Efficinecy is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity ratio is 20.0\n", + "Efficinecy is 90.0 %\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.17,Page No.314" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "P=40 #N #Effort\n", + "rho=0.5 #Efficincy\n", + "D=20 #cm #Dia. of load axle\n", + "L=80 #cm #Length of Lever\n", + "T1=10 #No. of teeth om pinion of effort axle\n", + "T2=100 #No. of teeth on spur wheel of intermediate axle\n", + "T3=20 #No. of teeth om pinion of Load axle\n", + "T4=200 #No. of teeth on spur wheel of load axle\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*L*D**-1*T2*T1**-1*T4*T3**-1 \n", + "\n", + "#Mechanical Advatnage\n", + "MA=rho*VR\n", + "\n", + "#Load Which can be Lifted\n", + "W=MA*P*10**-3 #N\n", + "\n", + "#Result\n", + "print\"Velocity ratio is\",round(VR,2)\n", + "print\"Load Which can be Lifted is\",round(W,2),\"KN\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity ratio is 800.0\n", + "Load Which can be Lifted is 16.0 KN\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.17(A),Page No.315" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "rho=0.4 #Efficincy\n", + "D=20 #cm #Dia. of load axle\n", + "L=40 #cm #Length of Lever\n", + "T1=15 #No. of teeth om pinion of effort axle\n", + "T2=45 #No. of teeth on spur wheel of intermediate axle\n", + "T3=20 #No. of teeth om pinion of Load axle\n", + "T4=40 #No. of teeth on spur wheel of load axle\n", + "W=250 #N #Load Lifted\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=VR=2*L*D**-1*T2*T1**-1*T4*T3**-1 \n", + "\n", + "#Effort applied\n", + "P=W*(rho*VR)**-1 #N\n", + "\n", + "#Result\n", + "print\"Effort applied at the end is\",round(P,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort applied at the end is 26.04 N\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.18,Page No.318" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "n=4 #No. of movable pulleys\n", + "W=1440 #N #Load\n", + "P=100 #N #effort\n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical Advantage\n", + "MA=W*P**-1 \n", + "\n", + "#Velocity ratio\n", + "VR=2**4\n", + "\n", + "#Efficiency\n", + "rho=MA*VR**-1*100 #%\n", + "\n", + "#Ideal Effort\n", + "P2=W*VR**-1\n", + "\n", + "#Effort wsted in friction\n", + "P3=P-P2 #N\n", + "\n", + "#Load WAsted in friction\n", + "W2=VR*P\n", + "\n", + "W3=W2-W\n", + "\n", + "#Result\n", + "print\"Efficiency of the machine is,\",round(rho,2),\"%\"\n", + "print\"Effort Wasted in friction is\",round(P3,2),\"N\"\n", + "print\"Load Wasted in friction is\",round(W3,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Efficiency of the machine is, 90.0 %\n", + "Effort Wasted in friction is 10.0 N\n", + "Load Wasted in friction is 160.0 N\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.19,Page No.320" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=2000 #N #Weight\n", + "P=600 #Effort\n", + "n=5 #Total No. of pulleys\n", + "VR=n \n", + "\n", + "#Calculations\n", + "\n", + "#Mechanical advantage\n", + "MA=W*P**-1\n", + "\n", + "#efficiency\n", + "rho=MA*VR**-1*100\n", + "\n", + "#Result\n", + "print\"Efficiency of the system is\",round(rho,2),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Efficiency of the system is 66.67 %\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.20,Page No.321" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "n=4 #No. of pulleys\n", + "P=160 #N #Effort\n", + "rho=0.75 #efficiency\n", + "VR=15 #Velocity ratio\n", + "\n", + "#Calculations\n", + "\n", + "#weight Lifted\n", + "W=rho*P*VR \n", + "\n", + "#Result\n", + "print\"Weight Lifted is\",round(W,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Weight Lifted is 1800.0 N\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.21,Page No.323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "rho=0.5 #Efficency\n", + "D=25 #cm #Diameter of Large pulley\n", + "d=20 #cm #Dia. of smaller pulley\n", + "P=20 #N #Effort applied\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*D*(D-d)**-1\n", + "\n", + "#Load Lifted\n", + "W=rho*d*VR #N\n", + "\n", + "#Result\n", + "print\"Load Lifted by the machine is\",round(W,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Load Lifted by the machine is 100.0 N\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.22,Page No.327" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=1500 #Load\n", + "L=0.7 #Length of handle\n", + "d=0.06 #m #Mean diaof screw jack\n", + "p=0.009 #pitch of the screw jack\n", + "mu=0.095 #co-efficient of friction\n", + "pi=3.14\n", + "\n", + "#Calculations\n", + "\n", + "#Effort required\n", + "X=(W*d*(2*L)**-1)*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n", + "\n", + "#Effort required at the end of the handle for lowering the load\n", + "P2=W*d*(2*L)**-1*(mu*pi*d-p)*(pi*d+mu*p)**-1 #N\n", + "\n", + "#Result\n", + "print\"Effort required at the end of the handle for Lifting Load 1500 N\",round(X,2),\"N\"\n", + "print\"Effort required at the end of the handle for lowering the load is\",round(P2,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort required at the end of the handle for Lifting Load 1500 N 9.22 N\n", + "Effort required at the end of the handle for lowering the load is 3.02 N\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.23,Page No.328" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=3000 #N #Load Lifted\n", + "n=2 #No. of square thread\n", + "D1=6 #cm #Outer diameter\n", + "mu=0.09 #Coefficient offriction\n", + "L=0.6 #m #Length\n", + "\n", + "#Calculations\n", + "\n", + "#pitch of screw\n", + "p=1.2*n**-1*10**-2 #m\n", + "\n", + "#Thickness of thread\n", + "t=0.5*p #\n", + "\n", + "#Diameter at base of screw\n", + "D2=D1-2*t\n", + "\n", + "#Mean Diameter\n", + "d=(D1+D2)*2**-1*10**-2 #m\n", + "\n", + "#Force \n", + "P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n", + "\n", + "#Result\n", + "print\"Force required at the end of handle is\",round(P,2),\"N\"\n", + "\n", + "#Answer in textbook is incorrect" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force required at the end of handle is 18.32 N\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.23(A),Page No.328" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=5000 #N #Load\n", + "n=2\n", + "t=0.003 #m #Thickness\n", + "D1=0.06 #m #outer diameter\n", + "D2=0.054 #m #Inner diameter\n", + "d=0.057 #MEan diameter\n", + "mu=0.08 #Coefficient of friction\n", + "L=0.6 #m #Length\n", + "p=0.006 #m #pitch\n", + "\n", + "#Calculations\n", + "\n", + "#Let tan(alpha)=X\n", + "X=p*(pi*d)**-1\n", + "\n", + "#Let tan(phi)=Y\n", + "Y=mu\n", + "\n", + "#Force reuired at the end of handle \n", + "P=d*(2*L)**-1*W*(X+Y)*(1-X*Y)**-1\n", + "\n", + "#Result \n", + "print\"Force reuired at the end is\",round(P,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force reuired at the end is 27.03 N\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.24,Page No.329" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "W=2000 #N #Load Lifted\n", + "p=1 #mm #pitch\n", + "rho=0.5 #efficiency\n", + "L=50 #cm #Length of handle\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*pi*L*p**-1\n", + "\n", + "#Effort applied\n", + "P=W*(rho*VR)**-1\n", + "\n", + "#Result\n", + "print\"Effort applied at the end of handle\",round(P,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort applied at the end of handle 12.74 N\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.25,Page No.332" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "rho=0.55 #efficiency\n", + "W=1500 #N #Load Lifted\n", + "L=0.5 #m #Length of handle\n", + "p=0.01 #m #Pitch of the screw\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*pi*L*p**-1 \n", + "\n", + "#Effort applied\n", + "P=W*(VR*rho)**-1 #N\n", + "\n", + "#Result\n", + "print\"Effort applied is\",round(P,2),\"N\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort applied is 8.69 N\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.26,Page No.333" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "d=0.075 #m #Mean diameter\n", + "p=0.015 #m #Pitch of threads\n", + "mu=0.05 #Coefficient of friction\n", + "W=600 #N\n", + "L=0.36 #m #LEngth\n", + "\n", + "#Calculations\n", + "\n", + "#Tangential Force\n", + "P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n", + "\n", + "#Let Tan(alpha)=X\n", + "#tan(phi)=Y\n", + "#tan(alpha+phi)=Z\n", + "X=p*(pi*d)**-1\n", + "Y=mu\n", + "Z=(X+Y)*(1-X*Y)**-1\n", + "\n", + "#efficiency\n", + "rho=X*Z**-1 \n", + "\n", + "#Effort\n", + "P2=W*((X-Y)*(1+X*Y)**-1) #N\n", + "\n", + "#Torque required\n", + "T=P2*d*2**-1 #N*m\n", + "\n", + "#Result\n", + "print\"Tangential Force to be qpplied is\",round(P,2),\"N\"\n", + "print\"Torque necesscary to lower the load is\",round(T,2),\"Nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Tangential Force to be qpplied is 7.13 N\n", + "Torque necesscary to lower the load is 0.31 Nm\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.27,Page No.334" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "d=0.06 #m #Mean diameter\n", + "p=0.008 #m P#itch\n", + "mu=0.09\n", + "W=3 #Load Lifted\n", + "x=0.12 #m\n", + "n=15 #No. of turns\n", + "\n", + "#Calculations\n", + "\n", + "#Let Tan(alpha)=X\n", + "#tan(phi)=Y\n", + "X=p*(pi*d)**-1\n", + "Y=mu\n", + "P=W*((X+Y)*(1-X*Y)**-1) #N\n", + "\n", + "#Torque required\n", + "T=P*d*2**-1 #N*m\n", + "\n", + "#Total Angular displacement\n", + "omega=n*2*pi\n", + "\n", + "#Workk done\n", + "W2=omega*T #KNm\n", + "\n", + "#efficiency\n", + "rho=W*x*W2**-1*100 #%\n", + "\n", + "#Efficiency can also be determined as\n", + "rho2=X*(X+Y)**-1*(1-X*Y)*100\n", + "\n", + "#Result\n", + "print\"Torque required is\",round(T,2),\"Nm\"\n", + "print\"Work done in lifting the load is\",round(W2,3),\"KN\"\n", + "print\"Efficiency of the jack is\",round(rho2,1),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Torque required is 0.01 Nm\n", + "Work done in lifting the load is 1.127 KN\n", + "Efficiency of the jack is 31.9 %\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.28,Page No.336" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from math import sin, cos, tan, radians, pi\n", + "\n", + "#Initilization of Variables\n", + "\n", + "p1=1 #cm #Pitch of Larger screw\n", + "p2=0.7 #cm #Pitch of smaller screw\n", + "l=36 #cm #Length of handle\n", + "rho=0.28 #efficiency\n", + "W=5000 #N #Weight\n", + "\n", + "#Calculations\n", + "\n", + "#Velocity ratio\n", + "VR=2*pi*l*(p1-p2)**-1\n", + "\n", + "#Effort applied\n", + "P=W*(rho*VR)**-1 #N\n", + "\n", + "#Result\n", + "print\"Effort required to Lift the Load\",round(P,2),\"N\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Effort required to Lift the Load 23.68 N\n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit